Systems analysis by graphs and matroids. Structural solvability and controllability
type: Item
instance of: scholarly article
title: Systems analysis by graphs and matroids. Structural solvability and controllability
zbMATH Open document ID: 0624.05001
author: Kazuo Murota
published in: Algorithms and Combinatorics
publication date: 1987-01-01T00:00:00Z
review text: Graph theory, as a branch of combinatorial mathematics has achieved remarkable development in the past several decades, leading to fruitful generalizations and extensions such as network theory and matroid theory. It has become widely recognized that some of the concepts and results in combinatorics serve also as useful mathematical tools for the analysis of engineering systems. This book is a monograph devoted to the study of the structural analysis of systems of linear or nonlinear equations and to that of the structural controllability of linear time-invariant dynamical systems through graph- theoretic models. The major usefulness of the presented theory seems to be oriented to the case of large-scale dynamical systems. The reader will become acquainted with the concepts of matroid theory and its corresponding matroid theoretic approach. This book is of interest to graduate students and researchers. Chapter 1 is devoted to mathematical preliminaries along with conventions. Algebraic concepts concerning algebraic independence and ranks of matrices are introduced. Basic concepts about matroids as pairs of a finite set and a collection of subsets with a set of properties are given along with relevant results in graph theory and matroid theory such as Dulmage-Mendelsohn decomposition of bipartite graphs. The principal partition of submodular functions is mentioned with some emphasis on the algorithmic aspects. In Chapter 2, a graph-theoretic method is developed for the structural analysis of a system of linear/nonlinear equations. In particular, a sound mathematical basis is given to some of the graphical techniques that have been successfully incorporated in some chemical process simulators developed in Japan. In particular examples on: (a) A reactor- separator model, (b) Hydrogen production system of application of the graphical technique are given subsequently. In Chapter 3, graph-theoretic conditions are given to the structural controllability of a linear dynamic…
Mathematics Subject Classification ID: 05-02
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 93A05
Mathematics Subject Classification ID: 94C15
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15A03
zbMATH DE Number: 4012613
zbMATH Keywords: systems of linear or nonlinear equations
zbMATH Keywords: controllability of linear time- invariant dynamical systems
zbMATH Keywords: graph-theoretic models
zbMATH Keywords: matroid theory
reviewed by: M. De la Sen
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4012613